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I guess this depends more on how the brain processes the signal rather than on how the eyes detect it. So technically, it might be possible but I'm not sure if there is a way to know. You can't go around asking animals how their brains work :)
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Ondřej ČernotíkDec 19 '12 at 9:29

2 Answers
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Many creatures have eyes on the sides of their head where they cannot have both eyes simultaneously look at the same target. For example whales. Chameleons are well known for having independently moving eyes (though they can align them for binocular vision)

Since all the significant processing of vision occurs in the brain's occipital lobes there is no problem with optics.

spiders usually have two rows of 4 eyes each, so they are not really vertical, but more hemispherical at least. They eyes don't see very well... in the case of jumping spiders they seem to lose the top row...
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shigetaDec 19 '12 at 14:20

The answer depends on the distance between eyes, and width of the objects you are viewing.

The view of a separate object is close to the orthogonal view when the width of the object is equal to the distance between your eyes.

Hence the creature that has variable distance between eyes, and has large maximum distance between eyes, has most possibilities to view objects in orthogonal view. Snail comes to mind when I try to think about animal with variable distance between eyes, but its maximum distance between eyes is not that large.

When object is narrower than distance between eyes, you see it in "anti-panoramic view". You will see both left and right side of the object, which is impossible both in orthogonal view and in panoramic view.

Speaking about whole 180 degrees wide visble scene (wider for some animals), the answer is No. You cannot view the whole scene without perspective view, unless you have large number of "eyes" (sensors) that are spread over a large plane. There is no such animal, but you can artificially construct such "perceptor plane" using large number of photocameras.

When looking at the objects of width equal to distance between eyes, if your brain can direct eyes such that their viewing axes are parallel, and could integrated two pictures, then it would view perfectly orthogonal view. This is not what our brain normally does, though. But even with non-parallel view axes of eyes, what we eventually see when brain integrates different pictures the result is not par from orthogonal projection.